On the Vacuum Structure of the <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Conformal Supergravity

We consider <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math><...

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Autores principales:	Ioannis Dalianis, Alex Kehagias, Ioannis Taskas, George Tringas
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	supergravity conformal symmetry weyl gravity conformal supergravity Elementary particle physics QC793-793.5
Acceso en línea:	https://doaj.org/article/b9196fa6a62747739d23a6e66620fbd1
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spelling	oai:doaj.org-article:b9196fa6a62747739d23a6e66620fbd12021-11-25T19:09:32ZOn the Vacuum Structure of the <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Conformal Supergravity10.3390/universe71104092218-1997https://doaj.org/article/b9196fa6a62747739d23a6e66620fbd12021-10-01T00:00:00Zhttps://www.mdpi.com/2218-1997/7/11/409https://doaj.org/toc/2218-1997We consider <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> conformal supergravity with an arbitrary holomorphic function of the complex scalar <i>S</i> which parametrizes the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>/</mo><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> coset. Assuming non-vanishings vevs for <i>S</i> and the scalars in a symmetric matrix <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></semantics></math></inline-formula> of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mn mathvariant="bold">10</mn><mo>¯</mo></mover></semantics></math></inline-formula> of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><mo>)</mo></mrow></semantics></math></inline-formula> R-symmetry group, we determine the vacuum structure of the theory. We find that the possible vacua are classified by the number of zero eigenvalues of the scalar matrix and the spacetime is either Minkowski, de Sitter, or anti-de Sitter. We determine the spectrum of the scalar fluctuations and we find that it contains tachyonic states which, however, can be removed by appropriate choice of the unspecified at the supergravity level holomorphic function. Finally, we also establish that <i>S</i>-supersymmetry is always broken whereas <i>Q</i>-supersymmetry exists only on flat Minkowski spacetime.Ioannis DalianisAlex KehagiasIoannis TaskasGeorge TringasMDPI AGarticlesupergravityconformal symmetryweyl gravityconformal supergravityElementary particle physicsQC793-793.5ENUniverse, Vol 7, Iss 409, p 409 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	supergravity conformal symmetry weyl gravity conformal supergravity Elementary particle physics QC793-793.5
spellingShingle	supergravity conformal symmetry weyl gravity conformal supergravity Elementary particle physics QC793-793.5 Ioannis Dalianis Alex Kehagias Ioannis Taskas George Tringas On the Vacuum Structure of the <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Conformal Supergravity
description	We consider <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> conformal supergravity with an arbitrary holomorphic function of the complex scalar <i>S</i> which parametrizes the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo><mo>/</mo><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> coset. Assuming non-vanishings vevs for <i>S</i> and the scalars in a symmetric matrix <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></semantics></math></inline-formula> of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mn mathvariant="bold">10</mn><mo>¯</mo></mover></semantics></math></inline-formula> of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><mo>)</mo></mrow></semantics></math></inline-formula> R-symmetry group, we determine the vacuum structure of the theory. We find that the possible vacua are classified by the number of zero eigenvalues of the scalar matrix and the spacetime is either Minkowski, de Sitter, or anti-de Sitter. We determine the spectrum of the scalar fluctuations and we find that it contains tachyonic states which, however, can be removed by appropriate choice of the unspecified at the supergravity level holomorphic function. Finally, we also establish that <i>S</i>-supersymmetry is always broken whereas <i>Q</i>-supersymmetry exists only on flat Minkowski spacetime.
format	article
author	Ioannis Dalianis Alex Kehagias Ioannis Taskas George Tringas
author_facet	Ioannis Dalianis Alex Kehagias Ioannis Taskas George Tringas
author_sort	Ioannis Dalianis
title	On the Vacuum Structure of the <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Conformal Supergravity
title_short	On the Vacuum Structure of the <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Conformal Supergravity
title_full	On the Vacuum Structure of the <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Conformal Supergravity
title_fullStr	On the Vacuum Structure of the <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Conformal Supergravity
title_full_unstemmed	On the Vacuum Structure of the <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Conformal Supergravity
title_sort	on the vacuum structure of the <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">n</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> conformal supergravity
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/b9196fa6a62747739d23a6e66620fbd1
work_keys_str_mv	AT ioannisdalianis onthevacuumstructureoftheinlineformulamathdisplayinlinesemanticsmrowmimathvariantscriptnmimomomn4mnmrowsemanticsmathinlineformulaconformalsupergravity AT alexkehagias onthevacuumstructureoftheinlineformulamathdisplayinlinesemanticsmrowmimathvariantscriptnmimomomn4mnmrowsemanticsmathinlineformulaconformalsupergravity AT ioannistaskas onthevacuumstructureoftheinlineformulamathdisplayinlinesemanticsmrowmimathvariantscriptnmimomomn4mnmrowsemanticsmathinlineformulaconformalsupergravity AT georgetringas onthevacuumstructureoftheinlineformulamathdisplayinlinesemanticsmrowmimathvariantscriptnmimomomn4mnmrowsemanticsmathinlineformulaconformalsupergravity
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On the Vacuum Structure of the <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></semantics></math></inline-formula> Conformal Supergravity

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